Descriptive Statistics

Remember that statistics is a process. We always begin with a question that we wish to answer. Chapter 1 started with the identifying the question and the relevant population and continued with methods of obtaining the data (steps 1 and 2 in the process). Descriptive statistics is the branch of statistics where we organize and summarize the data, step 3 in the process. Descriptive statistics combines the graphical organization methods that we introduced in chapter 2 with numerical summary statistics that we introduce in chapter 3.

Figure 3.1: The process of statistics, step 3.

When we summarize quantitative data in descriptive statistics, we will address the following 4 characteristics, all of which are discussed in chapter 3.

•Center- a way to describe the middle, or most typical.

•Variation- a way to describe how much the data varies.

•Shape of the distribution- methods to describe features of the distribution.

•Outliers- are there any highly unusual values?

Section 3.1 will discuss measures of center, while section 3.2 covers measures of variation. Section 3.3 will cover measures of position within a distribution and how the shape determines the best statistics to apply. Section 3.4 will present outliers and a new graph called a boxplot.

By the end of this chapter, you will be able to:

•Describe, calculate, and interpret measurements of center, including

▪the mean

▪the median

▪the mode

•Describe, calculate, and interpret measurements of variation or dispersion, including

▪the range

▪the standard deviation

▪the variance

▪the interquartile range

•Describe, calculate, and interpret measures of relative position, including

▪z-scores

▪percentile rank

▪quartiles

•Find the 5-number summary of a data set

•Identify and describe outliers

•Create and interpret a boxplot for a data set

•Identify the circumstances when each of these measures is appropriate to use.